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arXiv · 2005.14018

Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs

Tim Graefnitz
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Abstract

Consider a log Calabi-Yau pair $(X,D)$ consisting of a smooth del Pezzo surface $X$ of degree $\geq 3$ and a smooth anticanonical divisor $D$. We prove a correspondence between genus zero logarithmic Gromov-Witten invariants of $X$ intersecting $D$ in a single point with maximal tangency and the consistent wall structure appearing in the dual intersection complex of $(X,D)$ from the Gross-Siebert reconstruction algorithm. More precisely, the logarithm of the product of functions attached to unbounded walls in the consistent wall structure gives a generating function for these invariants.

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Tim Graefnitz. 2020-05-28. Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs. https://arxiv.org/abs/2005.14018

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